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- The cost formula for a company can be modeled by C=1092+40x+0.1x2C=1092+40x+0.1x2 where xx represents the number of items made. A formula for the company's income is modeled with R=108x−0.9x2R=108x-0.9x2, where xx is the number of items sold. A company will break even when its costs equal its income. How many items must a company make and then sell to break even? Answer: (If there are multiple answers, separate the answers with a comma.)You are analyzing a new company’s records projecting their profits using a marginal profit function, P′(x), where P is profit, in thousands of dollars, and x is the number of items they sell, in hundreds. the integral is from 5 to 1 for P ′(x) dx = 22. If the company projects to earn $26,000 of profit from selling 500 items and $7000 of that revenue from selling 100 items, what is their projected cost from selling 100 items?The profit made by selling q1 units of product 1 and q2 units of product 2 is given by P(q1,q2)=200q1 −3q12 +100q2 −q2 −2q1q2 (a) Calculate ∂P (20, 15) and ∂P (20, 15). ∂q1 ∂q2 (b) Describe the graphical meaning of these two numbers. (c) Describe the economic meaning of these two numbers. (d) Find a linear function g(q1, q2) that can be used as an approximation for the function P (q1, q2) for values (q1,q2) close to (20,15). Explain how the function g(q1,q2) relates to the function P(q1,q2) graphically. What is the mathematical name of the approximating function g? (e) Use the linear function you found in part d to estimate the profit made by selling 18 units of product 1 and 16 units of product 2. Compare to the exact value of the profit.
- Marginal revenue of a product is the incremental revenue of selling an additionalunit of that product. Let, the revenue of selling 20 units of a product beRs. 15,000 and the revenue of selling 21 units of the same product beRs. 15,085. Then, the marginal revenue of selling the 21st unit____?A cob Douglas production function for a firm is given as Q=4L ½K½. The firm has also established that wage rate and interest paid on capital are $3 and $5 respectively for a production period. The firm intents to spend $200 million for the period on production cost. Compute the levels of capital and labor that will maximize output. What is the maximum output?Ike's Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company's short-run average total cost (SRATC) each month for various levels of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.) NOTE: the options for the blank question is this Suppose Ike's Bikes is expecting to produce 500 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using _______ (once factory OR two factory OR three factory)
- Q1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two marketsThe manager's job in leading the previously mentioned production process is twofold: (1) toguarantee that the company works on the production function, and (2) to ensure that thebussiness employs the appropriate level of inputs. Justify how these two factors contribute tothe company operating at he optimal position the production function.Solve it correctly last time incorrect solution provides Q) The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimized
- Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimizedFirm ABC has estimated that it has the following production function: Q = 1.5LK – 0.3L2 – 0.15K2 Labor (L) has a price of €60 and capital (K) has a price of €75. ABC wants to maximize the production with a total cost of €2025. (a) Determine the quantities of labor and capital the firm should use. (round results to 2 decimal places) (b) What quantity of output will be produced at the optimal combination of factors of production?If the total cost for producing widgets can be represented by TC = 8,000 + 0.75*X, where X is the number of widgets produced and total revenue can be represented by TR = 4.00*X, what is the break-even value for number of widgets produced? a. 1,684 b. 2,000 c. 2,462 d. 3,763